Abstract:Cost-sensitive ranking support vector machine converts the order relation of samples into the classification relation of sample pairs, and it is particularly well suited to web information retrieval. However, learning large amounts of sample pairs takes extremely long time. A cost-sensitive smooth ranking support vector machine(cs-sRSVM) using 2-Norm error is presented. Firstly, the optimization object is transformed into unconstrained problem. Secondly, the smooth piecewise polynomial function is approximated to the hinge loss function. Finally, the unique optimal solution is obtained by applying Newton-YUAN method. The experimental results on a public dataset LETOR show that the training time of cs-sRSVM is faster than that of the existing cost-sensitive ranking algorithm, and its retrieval performance is equally impressive.
[1] Joachims T. Optimizing Search Engines Using Click through Data// Proc of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Edmonton, Canada, 2002: 133-142 [2]Svore K, vander Wende L, Burges C J C. Using Signals of Human Interest to Enhance Single-Document Summarization // Proc of the 23rd AAAI Conference on Artificial Intelligence. Chicago, USA, 2008: 1577-1580 [3]Gao Yongmei, Huang Yalou, Ni Weijian, et al. A Ranking SVM Based Algorithm for Automatic Extraction of Acronym. Pattern Recognition and Artificial Intelligence, 2008, 21(2): 186-192 (in Chinese) (高永梅,黄亚楼,倪维健,等.基于排序支持向量机的缩略词自动提取方法.模式识别与人工智能, 2008, 21(2): 186-192) [4]Chu W, Keerthi S S. Support Vector Ordinal Regression. Neural Computation, 2007, 19(3): 792-815 [5]Li Ping, Burges C J C, Wu Qiang. Mcrank: Learning to Rank Using Multiple Classification and Gradient Boosting // Proc of the 21st Annual Conference on Neural Information Processing Systems. Vancouver, Canada, 2007: 845-852 [6]Herbrich R, Graepel T, Obermayer K. Large Margin Rank Boundaries for Ordinal Regression // Proc of the 9th International Conference on Artificial Neural Networks. Edinburgh, UK, 1999: 97-102 [7]Xu Jun, Cao Yunbo, Li Hang, et al. Cost-Sensitive Learning of SVM for Ranking // Proc of the 17th European Conference on Machine Learning. Berlin, Germany, 2006: 833-840 [8]Cao Yunbo, Xu Jun, Liu Tieyan, et al. Adapting Ranking SVM to Document Retrieval // Proc of the 29th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. Seattle, USA, 2006: 186-193 [9]Burges C, Shaked T, Renshaw E, et al. Learning to Rank Using Gradient Descent // Proc of the 22nd International Conference on Machine Learning. Bonn, Germany, 2005: 89-96 [10]Guiver J, Snelson E. Learning to Rank with SoftRank and Gaussian Processes // Proc of the 31st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. Singapore, Singapore, 2008: 259-266 [11]Carvalho V R, Elsas J, Cohen W W, et al. A Meta-Learning Approach for Robust Rank Learning // Proc of the SIGIR Workshop on Learning to Rank for Information Retrieval. Singapore, Singapore, 2008: 15-23 [12]Cao Zhe, Qin Tao, Liu Tieyan, et al. Learning to Rank: From Pairwise Approach to Listwise Approach // Proc of the 24th Annual International Conference on Machine Learning. Corvallis, USA, 2007: 129-136 [13]Elsas J L, Carvalho V R, Carbonell J G. Fast Learning of Document Ranking Functions with the Committee Perceptron // Proc of the 1st ACM International Conference on Web Search and Data Mining. Palo Alto, USA, 2008: 55-64 [14]Zheng Zhaohui, Zha Honguan, Sun G. Query-Level Learning to Rank Using Isotonic Regression // Proc of the 46th Annual Allerton Conference on Communication, Control and Computing. Urbana-Champaign, USA, 2008: 1108-1115 [15]Zadrozny B. Learning and Evaluating Classifiers under Sample Selection Bias // Proc of the 21st International Conference on Machine Learning. Banff, Canada, 2004: 114-121 [16]Sheng V S, Ling C X. Thresholding for Making Classifiers Cost-Sensitive // Proc of the 21st National Conference on Artificial Intelligence. Boston, USA, 2006: 476-481 [17]Liu Tieyan, Xu Jun, Qin Tao, et al. LETOR: Benchmarking Learning to Rank for Information Retrieval // Proc of SIGIR Workshop on Learning to Rank for Information Retrieval. Amsterdam, Netherlands, 2007: 3-8 [18]Lee Y J, Mangasarian O L. SSVM: A Smooth Support Vector Machine. Computational Optimization and Applications, 2001, 20(1): 5-22 [19]Yuan Yubo, Yan Jie, Xu Chengxian. Polynomial Smooth Support Vector Machine (PSSVM). Chinese Journal of Computers, 2005, 28(1): 9-17(in Chinese) (袁玉波,严 杰,徐成贤.多项式光滑的支撑向量机.计算机学报, 2005, 28(1): 9-17) [20]Yuan Yaxiang. Step-Sizes for the Gradient Method // Proc of the 3rd International Congress of Chinese Mathematicians. Hongkong, China, 2004: 785-796 [21]Jrvelin K, Keklinen J. Cumulated Gain-Based Evaluation of IR Techniques. ACM Trans on Information Systems, 2002, 20(4): 422-446 [22]Huang C M, Lee Y J, Lin D, et al. Model Selection for Support Vector Machines via Uniform Design. Computational Statistics and Data Analysis, 2007, 52(1): 335-346